{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:S6YQVOIWFW3Q6O7VB6INVRTSP5","short_pith_number":"pith:S6YQVOIW","schema_version":"1.0","canonical_sha256":"97b10ab9162db70f3bf50f90dac6727f69b26c13a308b10741131f5ab60229a6","source":{"kind":"arxiv","id":"2605.16948","version":1},"attestation_state":"computed","paper":{"title":"Revisiting the Maximum Defective Clique Problem: Faster Branching and a Tighter Upper Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"BBRes speeds up exact search for maximum k-defective cliques by pruning tractable branches early.","cross_cats":[],"primary_cat":"cs.DB","authors_text":"Kaiqiang Yu, Kewu Yang, Shengxin Liu, Zhaoquan Gu","submitted_at":"2026-05-16T11:58:39Z","abstract_excerpt":"The $k$-defective clique model relaxes the strict completeness constraint of the traditional clique by allowing up to $k$ missing edges, providing a robust formulation for detecting cohesive structures in noisy graphs. Consequently, the maximum $k$-defective clique problem has attracted significant attention. State-of-the-art exact algorithms predominantly adopt the branch-and-bound framework, which recursively partitions the current problem instance (or branch) into two sub-problems via a branching procedure, until each sub-problem becomes trivially solvable. However, this strategy often lead"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.16948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2026-05-16T11:58:39Z","cross_cats_sorted":[],"title_canon_sha256":"c6b86b45251d6fc791c66eabab844f701ad420f70bcadfe51b4005cf06a7c5fd","abstract_canon_sha256":"0a6b69d562e69acffe1097650c590b322198e51e54181093ed9395c0f3efd80b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:32.385635Z","signature_b64":"/DP/P9p3BGdHwhpuLX5O73aCd9b8U6n679TqYIPCzMSDk3rSZaqLZaN7mYBvsX2PgYBKpB98qmhbODvhyiL1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97b10ab9162db70f3bf50f90dac6727f69b26c13a308b10741131f5ab60229a6","last_reissued_at":"2026-05-20T00:03:32.384877Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:32.384877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Revisiting the Maximum Defective Clique Problem: Faster Branching and a Tighter Upper Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"BBRes speeds up exact search for maximum k-defective cliques by pruning tractable branches early.","cross_cats":[],"primary_cat":"cs.DB","authors_text":"Kaiqiang Yu, Kewu Yang, Shengxin Liu, Zhaoquan Gu","submitted_at":"2026-05-16T11:58:39Z","abstract_excerpt":"The $k$-defective clique model relaxes the strict completeness constraint of the traditional clique by allowing up to $k$ missing edges, providing a robust formulation for detecting cohesive structures in noisy graphs. Consequently, the maximum $k$-defective clique problem has attracted significant attention. State-of-the-art exact algorithms predominantly adopt the branch-and-bound framework, which recursively partitions the current problem instance (or branch) into two sub-problems via a branching procedure, until each sub-problem becomes trivially solvable. However, this strategy often lead"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"BBRes achieves an improved theoretical worst-case time complexity and at least 2X speedup over state-of-the-art methods on a substantial fraction of the datasets.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The claim that a non-trivial fraction of intermediate sub-problems generated during branching are both non-trivial and solvable in polynomial time by the specialized solver, allowing the early-termination rule to prune the search tree without missing optimal solutions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"BBRes improves exact maximum k-defective clique search with early-termination branching and a tighter double-coloring-plus-max-flow upper bound, claiming better worst-case time and at least 2X empirical speedup on many instances.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"BBRes speeds up exact search for maximum k-defective cliques by pruning tractable branches early.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3b331225fa05b7b6a5c85cd841a318a2cc550b56d655843f0d238a4a993a8539"},"source":{"id":"2605.16948","kind":"arxiv","version":1},"verdict":{"id":"1badd9dc-24d7-40ef-9f28-578790ce9c36","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:04:06.536867Z","strongest_claim":"BBRes achieves an improved theoretical worst-case time complexity and at least 2X speedup over state-of-the-art methods on a substantial fraction of the datasets.","one_line_summary":"BBRes improves exact maximum k-defective clique search with early-termination branching and a tighter double-coloring-plus-max-flow upper bound, claiming better worst-case time and at least 2X empirical speedup on many instances.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The claim that a non-trivial fraction of intermediate sub-problems generated during branching are both non-trivial and solvable in polynomial time by the specialized solver, allowing the early-termination rule to prune the search tree without missing optimal solutions.","pith_extraction_headline":"BBRes speeds up exact search for maximum k-defective cliques by pruning tractable branches early."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16948/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T20:21:56.552627Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:18.922941Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:10:41.618919Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.240766Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.323943Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c1ee06bd1dc80ee50818029d66d133be153875878fb0200806c508d364a734b2"},"references":{"count":62,"sample":[{"doi":"","year":null,"title":"https://github.com/Thaumaturge2020/ BBRes/","work_id":"75519b28-383c-47e5-85d7-c0a1b902898a","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Mohiuddin Ahmed, Abdun Naser Mahmood, and Md Rafiqul Islam. 2016. A survey of anomaly detection techniques in financial domain.Future Generation Computer Systems55 (2016), 278–288","work_id":"1e6e1486-3fbe-413f-a0bf-2e6d7de6df91","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1993,"title":"Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin. 1993.Network Flows: Theory, Algorithms, and Applications. Prentice Hall","work_id":"acbde12c-ab27-4fc4-939b-921e4e1738d5","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"Ravindra K Ahuja and James B Orlin. 1995. A capacity scaling algorithm for the constrained maximum flow problem.Networks25, 2 (1995), 89–98","work_id":"8d2ba6cf-7740-481d-b4c7-313621cf9d93","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1993,"title":"Ravindra K Ahujia, Thomas L Magnanti, and James B Orlin. 1993. Network flows: Theory, algorithms and applications.New Jersey: Rentice-Hall3 (1993)","work_id":"15dbcd86-f05f-4c3c-ad49-bc5a34df806e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":62,"snapshot_sha256":"d3dca8fbcb6a83d0f1a8ae70c74a249c153b31f6bc517d0684ca5b2c4c6486ce","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"c0f7bdec2ce11070f2d92e21b93afb4a7b28ba15062f206ce6343061ef7d45c6"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.16948","created_at":"2026-05-20T00:03:32.384988+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.16948v1","created_at":"2026-05-20T00:03:32.384988+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16948","created_at":"2026-05-20T00:03:32.384988+00:00"},{"alias_kind":"pith_short_12","alias_value":"S6YQVOIWFW3Q","created_at":"2026-05-20T00:03:32.384988+00:00"},{"alias_kind":"pith_short_16","alias_value":"S6YQVOIWFW3Q6O7V","created_at":"2026-05-20T00:03:32.384988+00:00"},{"alias_kind":"pith_short_8","alias_value":"S6YQVOIW","created_at":"2026-05-20T00:03:32.384988+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S6YQVOIWFW3Q6O7VB6INVRTSP5","json":"https://pith.science/pith/S6YQVOIWFW3Q6O7VB6INVRTSP5.json","graph_json":"https://pith.science/api/pith-number/S6YQVOIWFW3Q6O7VB6INVRTSP5/graph.json","events_json":"https://pith.science/api/pith-number/S6YQVOIWFW3Q6O7VB6INVRTSP5/events.json","paper":"https://pith.science/paper/S6YQVOIW"},"agent_actions":{"view_html":"https://pith.science/pith/S6YQVOIWFW3Q6O7VB6INVRTSP5","download_json":"https://pith.science/pith/S6YQVOIWFW3Q6O7VB6INVRTSP5.json","view_paper":"https://pith.science/paper/S6YQVOIW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.16948&json=true","fetch_graph":"https://pith.science/api/pith-number/S6YQVOIWFW3Q6O7VB6INVRTSP5/graph.json","fetch_events":"https://pith.science/api/pith-number/S6YQVOIWFW3Q6O7VB6INVRTSP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S6YQVOIWFW3Q6O7VB6INVRTSP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S6YQVOIWFW3Q6O7VB6INVRTSP5/action/storage_attestation","attest_author":"https://pith.science/pith/S6YQVOIWFW3Q6O7VB6INVRTSP5/action/author_attestation","sign_citation":"https://pith.science/pith/S6YQVOIWFW3Q6O7VB6INVRTSP5/action/citation_signature","submit_replication":"https://pith.science/pith/S6YQVOIWFW3Q6O7VB6INVRTSP5/action/replication_record"}},"created_at":"2026-05-20T00:03:32.384988+00:00","updated_at":"2026-05-20T00:03:32.384988+00:00"}